Solve 2(x-2)(x-2)+4=2x^2-4x-6

$$2 ( x - 2 ) ( x - 2 ) + 4 = 2 x ^ { 2 } - 4 x - 6$$

Solve for x

$$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Steps for Solving Linear Equation

Multiply x-2 and x-2 to get \left(x-2\right)^{2}.

$$2\left(x-2\right)^{2}+4=2x^{2}-4x-6$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.

$$2\left(x^{2}-4x+4\right)+4=2x^{2}-4x-6$$

Use the distributive property to multiply 2 by x^{2}-4x+4.

$$2x^{2}-8x+8+4=2x^{2}-4x-6$$

Add 8 and 4 to get 12.

$$2x^{2}-8x+12=2x^{2}-4x-6$$

Subtract 2x^{2} from both sides.

$$2x^{2}-8x+12-2x^{2}=-4x-6$$

Combine 2x^{2} and -2x^{2} to get 0.

$$-8x+12=-4x-6$$

Add 4x to both sides.

$$-8x+12+4x=-6$$

Combine -8x and 4x to get -4x.

$$-4x+12=-6$$

Subtract 12 from both sides.

$$-4x=-6-12$$

Subtract 12 from -6 to get -18.

$$-4x=-18$$

Divide both sides by -4.

$$x=\frac{-18}{-4}$$

Reduce the fraction \frac{-18}{-4} to lowest terms by extracting and canceling out -2.

$$x=\frac{9}{2}$$